New Branches of Massive Gravity

Abstract

The basic building block for Lorentz invariant and ghost free massive gravity is the square root of the combination $g^{-1}\eta$, where $g^{-1}$ is the inverse of the physical metric and $\eta$ is a reference metric. Since the square root of a matrix is not uniquely defined, it is possible to have physically inequivalent potentials corresponding to different branches. We show that around Minkowski background the only perturbatively well defined branch is the potential proposed by de Rham, Gabadadze and Tolley. On the other hand, if Lorentz symmetry is broken spontaneously, other potentials exist with a standard perturbative expansion. We show this explicitly building new Lorentz invariant, ghost-free massive gravity potentials for theories that in the background preserve rotational invariance, but break Lorentz boosts.

5 pages

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• Failures of homogeneous and isotropic cosmologies in Extended Quasi-Dilaton Massive Gravity
• Massive gravity, canonical structure and gauge symmetry
• To Half--Be or Not To Be?
• Hamiltonian structure of bi-gravity, problem of ghost and bifurcation
• Theory of interacting vector dark energy and fluid
• Dealing with ghost-free massive gravity without explicit square roots of matrices
• Unusual square roots in the ghost-free theory of massive gravity
• Gauge generator for bi-gravity and multi-gravity models
• Algebraic aspects of massive gravity
• A note on the uniqueness of the dRGT massive gravity theory